Graphon mean-field backward stochastic differential equations with jumps and associated dynamic risk measures

Hamed Amini (), Zhongyuan Cao () and Agnès Sulem ()
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Hamed Amini: University of Florida
Zhongyuan Cao: NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
Agnès Sulem: INRIA Paris

Finance and Stochastics, 2025, vol. 29, issue 4, No 6, 1139-1194

Abstract: Abstract We study backward stochastic differential equations (BSDEs) with jumps with mean-field type heterogeneous interactions governed by graphons, and associated dynamic risk measures. We prove existence, uniqueness and measurability results of solutions of these systems under some regularity assumptions and provide moment estimates. Under additional conditions, comparison theorems are obtained. Continuity and stability of such systems are also established. We then prove convergence of finite interacting mean-field particle systems with heterogeneous interactions to graphon mean-field BSDEs. Finally, we introduce the graphon dynamic risk measure induced by the solution of a graphon mean-field BSDE system and study its properties. In particular, a dual representation theorem is provided in the convex case.

Keywords: Mean-field BSDEs with jumps; Heterogeneous interaction; Dynamic risk measures; 60K35; 05C80; 91B05 (search for similar items in EconPapers)
JEL-codes: C02 G32 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00780-025-00575-3

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